Toward Enhancing Stability and Agility of Dynamically Balancing Legged Robots: A Data-Driven Approach

For legged robots, to be practical, they need to be stable and agile. Stability is the ability to withstand perturbations, and agility is the ability to rapidly accelerate. Both this metrics are challenging to meet for dynamically balancing legged robots which are machines that have point feet or small feet and hence are statically unstable but need to constantly move to achieve dynamical stability. The most well-known method of stabilizing such robots is to generate a periodic or steady motion, also known as a limit cycle and then stabilizing the limit cycle. However, current techniques only provide small perturbation stability for the limit cycle limiting its usefulness. To generate agile gaits, non-steady motion needs to be planned, but is computationally challenging. Although steady state gaits are computationally simple to evaluate, such gaits are not agile. This thesis provides a framework for large perturbation stability of the limit cycle and composition of limit cycles to achieve agile locomotion. The framework is based on assuming a candidate Lyapunov function for step-to-step or orbital stability of the limit cycle. Then a data-driven approach is used to find a nonlinear control policy to stabilize the limit cycle and to estimate the set of initial states that can be stabilized also known as the region of attraction. These regions of attraction are composed using heuristics and sampling-based techniques to achieve agile motion. Finally, the thesis explores a computational approach for real-time planning on complex terrains such as stepping stones. The approach consists of using data-driven techniques to generate and model the step-to-step dynamics around the limit cycle. The resulting model is simple enough to enable real-time nonlinear optimization. Demonstration of these approaches is done using the spring-loaded inverted pendulum model of hopping and compass gait model of walking.